Hmmm, I don't think I understand. Let me try and run through a quick example and you can tell me what you mean. A and B are fighting. A rolls a 9 for Initiative, B rolls a 2. They are each armed with swords that take 3 ticks to swing, and you count Initiative down.
So, in a given round, A gets to start his swing at 9, complete his swing at 6, and then start another swing at 6 (or 5?) and then complete it at 3 (or 2), and so on. While poor B doesn't even get to swing his sword, I guess?
That strikes me as a less friendly version of Champions' venerable phase system, and a giant pain in the ass and all the wonky stuff I wrote above.
On the other hand, you could do something like how I recall AD&D's initiative system (note, I may totally be wrong, this is from 20+ years ago). Where the "ticks" system really mattered for interrupting people, which was really where the rubber hit the road. AD&D initiative counted upward, so suppose A rolled a 2 for Initiative and B rolled a 6. A begins his swing on 2, and then, if it's got a speed factor of 3, completes it on 5, before B even gets to start. Things get more interesting if A is using something with a large speed factor, like a greatsword, or a complicated spell, and B is using something light and quick like a dagger. You get the idea.
The small trick there is that by counting upward the round never "ended" till everyone got their chance to go. As a side note, rolling each round isn't too clunky, I don't think it'd even queer my 3E D&D games if I implemented that and it's got some advantages to it. But, it depends on how much happens in each round in the game. If it's quite a bit, then the rolling each time isn't so bad. If combats take place over many rounds, then it does add up.
I guess I'd ask, what are you aiming for out of the ticks system? It seems most appealing to me if you want a granular difference between options -- the greatsword v. dagger comparison. Otherwise, I think just allowing people on higher initiative counts to interrupt people going after them is a much simpler way to achieve the same ends. I alluded to Champions' phase system above. But, I think simply multiple actions -- either on a character's initiative or at the end of the round (a la White Wolf celerity) -- is a much easier way of getting that into a system.